$A$ charge $Q$ is placed at the center of a closed cube. The flux passing through any one face of the cube will be .......

$A$ sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$ whose center coincides with the given sphere. The flux related to the imaginary sphere is

If $\vec E = \frac{E_0 x}{a} \hat i$,then find the electric flux through the shaded area of the cube as shown in the figure,where the shaded face is at $x = a$.

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell,as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?
$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$
$(B)$ The $z$-component of the electric field is zero at all the points on the surface of the shell
$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$
$(D)$ The electric field is normal to the surface of the shell at all points

An electric line of force in the $X, Y-$ plane is given by the equation $x^2 + y^2 = 1$. $A$ particle with unit positive charge is initially at rest at the point $(1, 0)$ in the $X, Y-$ plane. The particle:

The figure shows the electric field lines around three point charges $A, B$,and $C$.
$(a)$ Which charges are positive?
$(b)$ Which charge has the largest magnitude? Why?
$(c)$ In which region or regions of the picture could the electric field be zero? Justify your answer.
$(i)$ Near $A$ $(ii)$ Near $B$ $(iii)$ Near $C$ $(iv)$ Nowhere